Related papers: Numerical Considerations for Advection-Diffusion P…
The accurate treatment of outflow boundary conditions remains a critical challenge in computational fluid dynamics when predicting aerodynamic forces and/or acoustic emissions. This is particularly evident when employing the lattice…
A numerical method is developed to efficiently calculate the stress (and displacement) field in finite 2D rectangular media. The solution is expanded on a function basis with elements that satisfy the Navier-Cauchy equation. The obtained…
Numerical simulation of multi-component flow systems characterized by the simultaneous presence of pressure-velocity coupling and pressure-density coupling dominated regions remains a significant challenge in computational fluid dynamics.…
Intracardiac flow patterns are shaped by the coupled motion of the cardiac chambers and heart valves and provide important information about cardiac function. However, clinical flow imaging remains limited by exam times, noise, resolution,…
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…
Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the…
The construction of weak solutions to compressible Navier-Stokes equations via a numerical method (including a rigorous proof of the convergence) is in a short supply, and so far, available only for one sole numerical scheme suggested in…
A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous…
We present and analyze in a unified setting two schemes for the numerical discretization of a Darcy-Forchheimer fluid flow model coupled with an advection-diffusion equation modeling the temperature distribution in the fluid. The first…
In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The stabilization is based on a graph-theoretic artificial…
The aim of this paper is to discuss the appropriate modelling of in- and outflow boundary conditions for nonlinear drift-diffusion models for the transport of particles including size exclusion and their effect on the behaviour of…
The aim of this study is to compare numerical methods for the simulation of single-phase flow and transport in fractured media, described here by means of the Discrete Fracture Network (DFN) model. A Darcy problem is solved to compute the…
In this letter we propose an optimization-based boundary controller for traffic flow dynamics capable of achieving both stability and invariance conditions. The approach is based on the definition of Boundary Control Barrier Functionals,…
Interfaces between two fluids are ubiquitous and of special importance for industrial applications, e.g., stabilisation of emulsions. The dynamics of fluid-fluid interfaces is difficult to study because these interfaces are usually…
We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method. The latter method is a now classical, finite…
In this study, we present a comprehensive numerical analysis of blood flow within human left ventricle models, with particular emphasis on optimizing simulation conditions to enhance the realism and computational efficiency of heart flow…
Mathematical modeling of fluid dynamics for computer graphics requires high levels of theoretical rigor to ensure visually plausible and computationally efficient simulations. This paper presents an in-depth theoretical framework analyzing…
The numerical stability of fluid flow is an important topic in computational fluid dynamics as fluid flow simulations usually become numerically unstable in the turbulent regime. Many mesh-based methods have already established numerical…
In the present study, an advection-diffusion problem has been considered for the numerical solution. The continuum equation is discretized using both upwind and centered scheme. The linear system is solved using the ILU preconditioned…
This dissertation resolves a longstanding discussion of a mathematical problem important in contaminant hydrogeology and chemical-reaction engineering, the proper mathematical description for a miscible solute undergoing longitudinal…